Optimization problem!!

You operate a bakery. You buy cakes from a supplier who charges you $6 per cake.
Government regulations dictate that you can only charge a price between $12 and $24
per cake. Your research shows that if you were to charge $x per cake, you would sell
180 x2
cakes per week.
(a) How much will you charge per cake?
(b) How much would you charge if there were no government regulations?

Re: Optimization problem!!

Yeah that sounds pretty weird that the government would impose a minimum price that you can charge. Every cake seller would ignore that and just charge the highest possible price--unless you introduce a demand constraint.

Edit: Oh ok I guess the research you talk about is the demand constraint. Hmmm let me think about this. Right off the bat we know that you cannot maximize profit since max profit occurs where the marginal cost ($6 in this case) equals the marginal revenue or selling price (which cannot fall below $12).